Factoring Polynomials by GCF and Grouping

Multiple Choice

Which of the following represents the factors of 12?

• 1, 12

• 1, 2, 3, 4, 6, 12

• 12, 24, 36, 48, 60

• No Factors

Multiple Choice

Which of the following represents the factors of 36?

• 1, 2, 3, 4, 6, 9, 12, 18, 36

• 36, 52, 108, 144

• No Factors

Greatest Common Factor

Definition : The biggest number that is a factor of each number!

Factors of 10: ​10, 1, 5, 2

​Factors of 5: 5, 1

​Largest factor in BOTH list: 5 The GCF is 5.

Finding the GCF of terms that include variables

• Find the largest number that divides evenly into all of the terms coefficients

• If all of the terms share the same variable(s) use those with the smallest exponent.

Poll

Find the GCF of

$$6x^2+10$$  

Coefficient of GCF is _____

Variable of GCF is  _____ 

GCF is _____

• Coefficient of GCF is 2, Variable of GCF is none,  GCF is 2

• 2, none, 2

Fill in the Blanks

Find the GCF of

$12x^2-18x$  

Coefficient of GCF is___  Variable of GCF is ___  GCF is ___

Separate answers with a comma.

Fill in the Blanks

Find the GCF of

$4x^2y-8xy^2$  

Coefficient of GCF ___ 

Variable of GCF ___

GCF __ 

Separate answers with a comma.

Multiple Select

Find the GCF of

$$6x^2y^3+9xy^2$$  

Coefficient GCF ___

Variable GCF ___

  Total GCF = 

• Coefficient GCF = 6

• Variable GCF =  $$xy^2$$  

• Coefficient GCF = 3

•  Total GCF =  $$3xy^2$$

Multiple Select

Find the GCF of

$$-15x^4y^2-25x^3y^3$$  

Coefficient GCF = 

Variable GCF = 

GCF = 

• Variable GCF =  $$x^3y^2$$  

• Variable GCF =  $$x^2y^3$$  

• Total GCF =  $$-5x^3y^2$$  

• Coefficient GCF = -5

Multiple Choice

What is the GCF of this expression:

$$10x^2-5$$  

• 10

• x

• 5

Multiple Choice

What is the GCF of this expression:

$$14r^{22}+7r^{22}$$  

• $$7r^{22}$$  

• 15

• No GCF

• Find the greatest common factor     (GCF).

• Divide the polynomial by the GCF. The quotient is the other factor.

• Express the polynomial as the product of the quotient and the GCF.

Factoring a polynomial means expressing it as a product of other polynomials.

Multiple Choice

Factor out the GCF

$$4x^2-8x-6$$  

• $$-3\left(x^2+5x-3\right)$$  

• $$2\left(2x^2-4x-3\right)$$  

Multiple Choice

Factor out the GCF

$$8x^3+12x^2-4x$$  

• $$2\left(4x^3+6x^2-4x\right)$$  

• $$4x\left(2x^2+3x-1\right)$$  

Multiple Choice

Factor out the GCF

$$2x^2y-4xy+6xy^2$$  

• $$2xy\left(x-2+3y\right)$$  

• $$-2xy\left(-xy^2+2-3y\right)$$  

Multiple Choice

Factor out the GCF

$$12x^4-16x^3+8x^2-28x$$  

• $$24x^2\left(5x-8xy^2+46x\right)$$  

• $$4x\left(3x^3-4x^2+2x-7\right)$$  

Multiple Choice

Which of the following is equivalent to w³ + 3w

• w (w²+3)

• 3w (w²+1)

• There is no GCF

Multiple Choice

Which of the following is equivalent to

$$4r^5+2r^3$$  

• $$r^3\left(4r^2+2\right)$$  

• $$2r^3\left(2r^2+1\right)$$  

• There is no GCF

Multiple Choice

x² + 8x + 2x + 16

• (x+2)(x+8)

• (x-2)(x-8)

• (x+1)(x+16)

• (x+6)(x+10)

Multiple Choice

Factor by grouping:

4p³ + 8p² + 3p + 6

• (2p²+3)(p+2)

• (2p²+6)(p+4)

• (4p²+3)(p+2)

• (4p²+8p)(3p+6)

Multiple Choice

Factor by grouping:

x³ + 7x² - 2x - 14

• (x²-2)(x-7)

• (x²+2)(x-7)

• (x²+2)(x+7)

• (x²-2)(x+7)

Multiple Choice

20x³ - 25x² + 4x - 5

• (5x²-5)(4x+1)

• 5(x²-1)(4x+5)

• (5x²+1)(4x-5)

• (5x²+1)(4x-1)